相关论文: Inverse Primitive Path Analysis

Primitive path analysis algorithms are now routinely employed to analyze entanglements in computer simulations of polymeric systems, but different analysis protocols result in different estimates of the entanglement length, N_e. Here we…

We combine computer simulations and scaling arguments to develop a unified view of polymer entanglement based on the primitive path analysis (PPA) of the microscopic topological state. Our results agree with experimentally measured plateau…

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

Several decades ago the Proximal Point Algorithm (PPA) started to gain a long-lasting attraction for both abstract operator theory and numerical optimization communities. Even in modern applications, researchers still use proximal…

We use recently developed primitive path analysis (PPA) methods to study the effect of equilibration on entanglement density in model polymeric systems. Values of N_e for two commonly used equilibration methods differ by a factor of two or…

Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…

In the literature, there are a few researches to design some parameters in the Proximal Point Algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via persistent homology, which encodes features of interest as…

Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed…

Drawing inspiration from the concept of the "primitive path" of a linear chain in melt conditions, we introduce here a numerical protocol which allows us to detect, in an unambiguous manner, the "primitive shapes" of ring polymers in…

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain…

We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…

In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is…

In engineering applications, line, circle, arc, and point are collectively referred to as primitives, and they play a crucial role in path planning, simulation analysis, and manufacturing. When designing CAD models, engineers typically…

Recently the field of inverse problems has seen a growing usage of mathematically only partially understood learned and non-learned priors. Based on first principles, we develop a projectional approach to inverse problems that addresses the…

We introduce an algorithm for the reduction of computer generated atomistic polymer samples to networks of primitive paths. By examining network ensembles of Polyethylene and cis-1,4 Polybutadiene melts, we quantify the underlying…

We develop Monte Carlo simulations for uniformly charged polymers and machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments.…

Finding a zero of a maximal monotone operator is fundamental in convex optimization and monotone operator theory, and \emph{proximal point algorithm} (PPA) is a primary method for solving this problem. PPA converges not only globally under…

Artificial intelligence (AI) promotes the polymer design paradigm from a traditional trial-and-error approach to a data-driven style. Achieving high thermal conductivity (TC) for intrinsic polymers is urgent because of their importance in…